Abstract
The answer set semantics may assign a logic program no model due to classic contradiction or cyclic negation. The latter can be remedied by resorting to a paracoherent semantics given by semi-equilibrium (SEQ) models, which are 3-valued interpretations that generalize the logical reconstruction of answer sets given by equilibrium models. While SEQ-models have interesting properties, they miss modularity in the rules, such that a natural modular (bottom up) evaluation of programs is hindered. We thus refine SEQ-models using splitting sets, the major tool for modularity in modeling and evaluating answer set programs. We consider canonical models that are independent of any particular splitting sequence from a class of splitting sequences, and present two such classes whose members are efficiently recognizable. Splitting SEQ-models does not make reasoning harder, except for deciding model existence in presence of constraints (without constraints, split SEQ-models always exist).
This work was partially supported by Regione Calabria under the EU Social Fund and project PIA KnowRex POR FESR 2007- 2013, and by the Italian Ministry of University and Research under PON project “Ba2Know (Business Analytics to Know) S.I.-LAB” n. PON03PE_0001.
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Amendola, G., Eiter, T., Leone, N. (2014). Modular Paracoherent Answer Sets. In: Fermé, E., Leite, J. (eds) Logics in Artificial Intelligence. JELIA 2014. Lecture Notes in Computer Science(), vol 8761. Springer, Cham. https://doi.org/10.1007/978-3-319-11558-0_32
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DOI: https://doi.org/10.1007/978-3-319-11558-0_32
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